No not correct. The tow vehicle should charge the battery. Check out this link:
You can see that pin number 4 is the battery charge terminal
Pushing the battery disconnect switch "in" does disconnect the battery from the trailer so in that case it won't charge via the TV, or from shore power either.
You should not tow with the battery disconnected however, if the trailer should come disengaged from the TV the battery is what provides power to the trailer brakes.